Multinomial Link Models

We propose a unified multinomial link model for analyzing categorical responses. It not only covers the existing multinomial logistic models and their extensions as a special class, but also allows the observations with NA or Unknown responses to be incorporated as a special category in the data analysis. We provide explicit formulae for computing the likelihood gradient and Fisher information matrix, as well as detailed algorithms for finding the maximum likelihood estimates of the model parameters. Our algorithms solve the infeasibility issue of existing statistical software on estimating parameters of cumulative link models. The applications to real datasets show that the proposed multinomial link models can fit the data significantly better, and the corresponding data analysis may correct the misleading conclusions due to missing data.